Explicit generators of the space of modular forms

Abstract

Let $S_κ$ be the space of cusp forms of weight $κ$ and level one, and let $S_κ^{\ast}$ denote its dual space. In this paper, we find explicit spanning subsets of $S_κ$ consisting of Rankin-Cohen brackets of Eisenstein series and explicit subsets of periods that span $S_κ^{\ast}$.